The phrase "going down the line" implies moving sequentially from one point to another, usually in a linear fashion. The antonyms for this phrase could include "diverging," "straying," or "veering off course." These terms suggest a deviation or departure from a set path or course of action. Other antonyms could be "standing still" or "remaining stationary," indicating a lack of movement or progression. Finally, the phrase "going up the line" could be seen as an antonym, suggesting movement in the opposite direction, potentially towards a different goal or endpoint. Ultimately, understanding the antonyms of a phrase is a helpful way to establish context and clarify meaning.